Algebra I EOC Extra Practice Halftime 12/13

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What is a system of inequalities?

Back

A system of inequalities is a set of two or more inequalities with the same variables. The solution is the set of all points that satisfy all inequalities in the system.

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How do you graph a system of inequalities?

Back

To graph a system of inequalities, first graph each inequality as if it were an equation. Then, shade the region that satisfies the inequality. The solution to the system is where the shaded regions overlap.

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What does the vertex of a parabola represent?

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The vertex of a parabola represents the highest or lowest point of the graph, depending on whether it opens upwards or downwards.

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How do you find the vertex of a quadratic function in standard form?

Back

For a quadratic function in standard form f(x) = ax^2 + bx + c, the vertex can be found using the formula x = -b/(2a) and then substituting this x-value back into the function to find the y-coordinate.

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What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce based on its domain.

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How do you determine the range of a linear function?

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For a linear function, the range is all real numbers unless there are restrictions on the domain.

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What is the difference between a strict inequality and a non-strict inequality?

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A strict inequality (e.g., < or >) does not include the boundary point, while a non-strict inequality (e.g., ≤ or ≥) includes the boundary point.

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What does it mean for a function to be increasing or decreasing?

Back

A function is increasing if its output values rise as the input values increase, and decreasing if its output values fall as the input values increase.

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What is the significance of the y-intercept in a linear equation?

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The y-intercept is the point where the graph of the equation crosses the y-axis, representing the output value when the input value (x) is zero.

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How do you solve a system of inequalities algebraically?

Back

To solve a system of inequalities algebraically, solve each inequality for the same variable and then find the intersection of the solutions.